This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To find the remainder when x^3 - 5x - 7 is divided by x+1, we can use the Remainder Theorem. Step 1: State the Remainder Theorem. The Remainder Theorem states that if a polynomial P(x) is divided by x-c, the remainder is P(c). Step 2: Identify the polynomial P(x) and the value of c. The given polynomial is P(x) = x^3 - 5x - 7. The divisor is x+1. To find c, we set the divisor to zero: x+1 = 0 x = -1 So, c = -1. Step 3: Substitute c = -1 into the polynomial P(x). The remainder is P(-1). P(-1) = (-1)^3 - 5(-1) - 7 Step 4: Calculate the value. P(-1) = -1 - (-5) - 7 P(-1) = -1 + 5 - 7 P(-1) = 4 - 7 P(-1) = -3 The remainder is -3.